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2006 A rational splitting of a based mapping space
Katsuhiko Kuribayashi, Toshihiro Yamaguchi
Algebr. Geom. Topol. 6(1): 309-327 (2006). DOI: 10.2140/agt.2006.6.309

Abstract

Let (X,Y) be the space of base-point-preserving maps from a connected finite CW complex X to a connected space Y. Consider a CW complex of the form Xαek+1 and a space Y whose connectivity exceeds the dimension of the adjunction space. Using a Quillen–Sullivan mixed type model for a based mapping space, we prove that, if the bracket length of the attaching map α:SkX is greater than the Whitehead length WL(Y) of Y, then (Xαek+1,Y) has the rational homotopy type of the product space (X,Y)×Ωk+1Y. This result yields that if the bracket lengths of all the attaching maps constructing a finite CW complex X are greater than WL(Y) and the connectivity of Y is greater than or equal to dimX, then the mapping space (X,Y) can be decomposed rationally as the product of iterated loop spaces.

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Katsuhiko Kuribayashi. Toshihiro Yamaguchi. "A rational splitting of a based mapping space." Algebr. Geom. Topol. 6 (1) 309 - 327, 2006. https://doi.org/10.2140/agt.2006.6.309

Information

Received: 19 July 2005; Revised: 14 February 2006; Accepted: 14 February 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1097.55010
MathSciNet: MR2220679
Digital Object Identifier: 10.2140/agt.2006.6.309

Subjects:
Primary: 55P62
Secondary: 54C35‎

Rights: Copyright © 2006 Mathematical Sciences Publishers

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